Derive an expression for the time dependence of the degree of polymerization for the stepwise polymerization of a hydroxyacid HO−R−COOH for which the rate law is d[A]/dt = −kr[A]2[OH], where A denotes the carboxylic acid group.
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Derive an expression for the time dependence of the degree of
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- Derive the integrated form of a third-order rate law v = kr[A]2[B] in which the stoichiometry is 2 A + B → P and the reactants are initially present in (a) their stoichiometric proportions ([B]0 = 12[A]0); (b) with B present initially in twice that amount ([B]0 = [A]0). Express your rate law in terms of [A]0, [B]0, and x, where [A] = [A]0 − 2x.The degradation of the antibiotic clindamycin stored at 343 K in aqueous solution at pH 4 is found to be first order with a rate constant of 2.49 x 10−7 s −1. Over the temperature range 320 K to 360 K theactivation energy was found to be 123.3 kJ mol−1. (a) Calculate the rate constant at 325 K.(b) The threshold for product safety is 1% degradation. At 295 K the time taken for 1% of the antibiotic to degrade is found to be close to 0.01/ k. Comment on the shelf-life of the drug.The rate law for the oxidation reaction 2CO(g) + O2(g) → 2CO2(g) assuming that the reaction occurs by the Langmuir -Hinshelwood mechanism. The over-all rate law for this mechanism is Rate = k3θCOθO2 ΘO2 = (KO2 [O2])1/2 and ΘCO = KCO [CO] --------------------------------- --------------------------------- 1+ (KO2[O2])1/2 + KCO[CO] 1+ (KO2[O2])1/2 + KCO[CO]
- In general for the reaction: cC + dD ➡️ aA + bB, write the rate law expression for reaction.In the hydrogenation of ethylene using a nickel catalyst, the initial concentration of ethylene is 1.70 mol⋅L^−1 and its rate constant (k) is 0.0010 mol⋅L^−1⋅s^−1 . Determine the rate of reaction if it follows a zero-order reaction mechanism.Derive the integrated form of a third-order rate law v = kr[A]2[B] in which the stoichiometry is 2 A +B −−→ P and the reactants are initially present in (a) their stoichiometric proportions, (b) with Bpresent initially in twice the amount.
- 2. Derive an expression for the time dependence of the degree of polymerization for the stepwise polymerization of a hydroxyacid HO – R- COOH for which the rate law is dA = -k,[A]²[0H] ,where A denotes the carboxylic acid group.Calculate the magnitude of the diffusion-controlled rate constant at 320 K for the recombination of two atoms in water, for which η = 0.89 cP. Assuming the concentration of the reacting species is 1.5 mmol dm−3 initially, how long does it take for the concentration of the atoms to fall to half that value? Assume the reaction is elementary.The rate constant for the reaction 2NO2 → 2NO + O2 is experimentally determined to be 0.153 mol−1 dm3 s −1 at 300°C and 0.993 mol−1 dm3 s −1 at 350°C. Estimate the effective radius of an NO2 molecule. The steric factor for this reaction is 0.05.
- The rate constant of the reaction H2O2(aq) + I−(aq) + H+(aq) → H2O(l) + HIO(aq) is sensitive to the ionic strength of the aqueous solution in which the reaction occurs. At 25 °C, kr = 12.2 dm6 mol−2 min−1 at an ionic strength of 0.0525. Use the Debye–Hückel limiting law to estimate the rate constant at zero ionic strength.Rate law experiments don’t always give data in the form of a rate in molesper second. Some of them give an amount of time necessary for areaction to proceed to a given point. The faster the rate, the less timenecessary. For the following data, assume that the time recorded for eachexperiment is the time required to consume 0.10 M of A in a hypotheticalreaction A + B yields C Time taken (s) [A]0 [B]0 36.8 0.20 0.40 25.0 0.20 0.60 10.0 0.50 0.60 Determine the rate law and the rate constant for the reactionThe adsorption of a gas is described by the Langmuir isotherm with α = 0.548 kPa−1 at 25 °C. Calculate the pressure at which the fractional surface coverage is (i) 0.20, (ii) 0.75.